Self-tuning in master–slave synchronization of high-precision stage systems

• A synchronization controller design having a two-filter FIR configuration.
• A data-driven self-tuning approach used to obtain the FIR coefficients in the context of Lur'e systems.
• An integral expression of the so-called feedforward sensitivity function used to pose a waterbed effect in which low-frequency suppression of the synchronization errors comes with high-frequency amplification of these errors.
• The synchronization controller design and parameter tunings subject to this waterbed effect being tested on an industrial case of reticle and wafer stage synchronization.

For synchronization of high-precision stage systems, in particular the synchronization between a wafer and a reticle stage system of a wafer scanner, a master–slave controller design is presented. The design consists of a synchronization controller based on FIR filters and a data-driven self-tuning approach is used to find the coefficients of these filters. In the context of Lur'e systems, i.e. the reticle stage slave system has a variable gain controller with saturation nonlinearity, a part of the gradients needed for self-tuning is obtained from reconstruction using closed-loop nonlinear models. The remaining part is given by sampled data obtained primarily from time-series measurements. Performance with the synchronization controller is shown to be bounded by a waterbed effect: low-frequency suppression comes at the price of high-frequency amplification. For the considered Lur'e stage systems the ability of the self-tuning to induce improved tracking is discussed in view of this waterbed effect for either simulation results or experimental results.